Method for processing tensor data for pattern recognition and computer device

ABSTRACT

A method for processing tensor data for pattern recognition and a computer device are provided. The method includes: constructing a decision function by the optimal projection tensor W which has been rank-one decomposed together with the offset scalar b, and inputting to-be-predicted tensor data which has been rank-one decomposed into the decision function for prediction.

FIELD OF THE INVENTION

The present application belongs to the technical field of patternrecognition, especially to a method for processing tensor data forpattern recognition and a computer device.

BACKGROUND OF THE INVENTION

With the advent of big data era, tensor expression of data has beenwidely used. However, during achieving the invention, the inventor foundout that in prior art vector model algorithm is still utilized toprocess tensor data. On the basis of the concept of vector modelalgorithm, during a preprocessing phase, feature extraction for originaldata (vectorization) should be performed, which firstly is easy todestroy spatial information and inner correlation which are specific totensor data, secondly possesses superabundant modern parameters whichwould easily lead to issues such as curse of dimensionality, overlearning and small amount of samples.

A plurality of tensor mode algorithms have become a trend of the era.However, solving an objective function of STM is a non-convexoptimization issue, in which solving by using an alternative projectionmethod is required; the time complexity of the algorithm is high and alocal minimum value occurs frequently.

SUMMARY OF THE INVENTION

In light of this, an embodiment of the invention provides a method forprocessing tensor data for pattern recognition and a computer device soas to solve the problems such as curse of dimensionality, over learningand small amount of samples occurred when the vector mode algorithmsprovided by the prior art process the tensor data and overcome theshortcomings of the tensor mode algorithms of the prior art. Thealgorithm of the invention aims at solve the limitations of thealgorithms of the prior art, for example, the time complexity of thealgorithms is high, and a local minimum value occurs frequently, etc.

On one hand, a method for processing tensor data for pattern recognitionis provided; the method includes:

receiving an input training tensor data set;

introducing a within class scatter matrix into an objective functionsuch that between class distance is maximized, at the same time, withinclass distance is minimized by the objective function;

constructing an optimal frame of the objective function of an optimalprojection tensor machine subproblem;

transforming N vector modes of quadratic programming subproblems into amultiple quadratic programming problem under a single tensor mode, andconstructing an optimal frame of an objective function of an optimalprojection tensor machine problem;

according to lagrangian multiplier method, obtaining a dual problem ofthe optimal frame of the objective function, introducing a tensor rankone decomposition into calculation of tensor transvection, and obtaininga revised dual problem;

utilizing sequential minimal optimization algorithm to solve the reviseddual problem and output an alagrangian optimal combination and an offsetscalar b;

calculating a projection tensor W_(*);

performing the rank one decomposition to the projection tensor W_(*);

performing a back projection to a component obtained after performingthe rank one decomposition to the projection tensor W_(*);

performing rank one decomposition inverse operation to the componentobtained after performing the back projection to obtain an optimalprojection tensor W which is corresponded to the training tensor dataset;

decision function construction phase: by the optimal projection tensor Wwhich has been rank-one decomposed together with the offset scalar b,constructing a decision function;

application prediction phase: inputting to-be-predicted tensor datawhich has been rank-one decomposed into the decision function forprediction.

Furthermore, after introducing the within class scatter matrix into anobjective function of an STM subproblem, through an eta coefficient theobjection function of the quadratic programming problem of an n-thsubproblem is changed into:

${\min\limits_{w^{(n)},b^{(n)},\zeta^{(n)}}{\frac{1}{2}\left\lbrack {\left( {{w^{(n)}}_{F}^{2} + {\eta\left( {\left( w^{(n)} \right)^{T}S_{w}^{(n)}w^{(n)}} \right)}} \right){\prod\limits_{1 < i < N}^{i \neq n}\;\left( {{w^{(i)}}_{F}^{2} + {\eta\left( {\left( w^{(i)} \right)^{T}S_{w}^{(n)}w^{(i)}} \right)}} \right)}} \right\rbrack}} + {C{\sum\limits_{m = 1}^{M}\;\xi_{m}^{(n)}}}$

wherein, S_(w) ^((n)) is an n-th order within class scatter matrixestimated after the training tensor data set is expanded along the n-thorder; w^((n)) is an n-th order optimal projection vector of thetraining tensor data, n=1, 2, . . . N; C is a penalty factor; ξ_(m)^((n)) is a slack variable; eta coefficient η is configured to measurethe importance of the within class scatter matrix.

Furthermore, the optimal frame of an objective function of an OPSTMproblem is a combination of N vector modes of quadratic programmingproblems, which respectively corresponds to a subproblem; wherein, aquadratic programming problem of an n-th subproblem is:

${\min\limits_{w_{*}^{(n)},b^{(n)},\xi^{(n)}}{\frac{1}{2}{w_{*}^{(n)}}_{F}^{2}{\prod\limits_{1 \leq i \leq N}^{i \neq n}\;{w_{*}^{(i)}}_{F}^{2}}}} + {C{\sum\limits_{m = 1}^{M}\;\xi_{m}^{(n)}}}$${y_{m}\left( {{\left( w_{*}^{(n)} \right)^{T}\left( {V_{m}{\prod\limits_{1 \leq i \leq N}^{i \neq n}\;{\times_{i}w_{*}^{(i)}}}} \right)} + b^{(n)}} \right)} \geq {1 - \xi_{m}^{(n)}}$S.t ξ_(m)^((n)) ≥ 0  m = 1, 2, …  M

wherein, w_(*) ^((n)) is the n-th order projection vector of thetraining tensor data set; w_(*) ^((n))=Λ^((n)1/2)P^((n)T)w^((n)),wherein Λ^((n)) and P^((n)) meet the equation, P^((n)T)(E+ηS_(w)^((n)))P^((n))=Λ^((n)); E is an identity matrix;

$V_{m} = {X_{m}{\prod\limits_{i = 1}^{N}\;{\times_{i}\left\lbrack \left( {P^{(i)}\Lambda^{{(i)}\;{1/2}}} \right)^{- 1} \right\rbrack^{T}}}}$is tensor input data obtained after tensor input data X_(m) in thetraining tensor data set is projected along each order; X_(i) is ani-mode multiplication operator; b^((n)) is the n-th order offset scalarof the training tensor data set.

Furthermore, according to a formula

${{W_{*}}_{F}^{2} = {\prod\limits_{n = 1}^{N}\;{w_{*}^{(n)}}_{F}^{2}}},$and a formula (w_(*) ^((n)))^(T)(V_(m)Π_(1<i<N) ^(i≠n)×_(i)w_(*)^((i)))=<W_(*), V_(m)>, transforming the N vector modes of quadraticprogramming subproblems into the multiple quadratic programmingsubproblem under a single tensor mode. A constructed optimal frame ofthe objective function of the OPSTM problem meets that:

${\min\limits_{{W_{*}b},\xi}{\frac{1}{2}{W_{*}}_{F}^{2}}} + {C{\sum\limits_{m = 1}^{M}\;\xi_{m}}}$y_(m)(⟨W_(*), V_(m)⟩ + b) ≥ 1 − ξ_(m)S.tξ_(m) ≥ 0  m = 1, 2, …  M

wherein, < > is a transvection operator, and

$\xi_{m} = {\max\limits_{{n = 1},2,\;{\ldots\mspace{11mu} N}}{\left\{ \xi_{m}^{(n)} \right\}.}}$

Furthermore, according to lagrangian multiplier method, an obtained dualproblem of the optimal frame of the objective function is:

${\max\limits_{\alpha}{\sum\limits_{m = 1}^{M}\;\alpha_{m}}} - {\frac{1}{2}{\sum\limits_{i,{j = 1}}^{M}\mspace{11mu}{\alpha_{i}\alpha_{j}y_{i}y_{j}\left\langle {V_{i},V_{j}} \right\rangle}}}$${{\sum\limits_{m = 1}^{M}\;\left( {\alpha_{m}y_{m}} \right)} = {{{0{S.t}0} < a_{m} < {C\mspace{14mu} m}} = 1}},2,{{\ldots\mspace{14mu} M};}$

introducing the tensor rank one decomposition into the calculation ofthe tensor transvection. An obtained revised dual problem is:

${\max\limits_{\alpha}{\sum\limits_{m = 1}^{M}\;\alpha_{m}}} - {\frac{1}{2}{\sum\limits_{i,{j = 1}}^{M}\;{\sum\limits_{p = 1}^{R}\;{\sum\limits_{q = 1}^{R}\;{\alpha_{i}\alpha_{j}y_{i}y_{j}{\sum\limits_{n = 1}^{N}\;\left\langle {v_{ip}^{(n)},v_{jq}^{(n)}} \right\rangle}}}}}}$${{\sum\limits_{m - 1}^{M}\;\left( {\alpha_{m}y_{m}} \right)} = {{{0{S.t}0} < \alpha_{m} < {C\mspace{14mu} m}} = 1}},2,{\ldots\mspace{14mu}{M.}}$

Furthermore, calculating the projection tensor W_(*) according to aformula,

$W_{*} = {\sum\limits_{m = 1}^{M}\;{\alpha_{m}y_{m}{V_{m}.}}}$

On the other hand, a computer device is provided. The computer deviceincludes a storage medium with computer instructions stored therein. Thecomputer instructions are configured to enable the computer device toexecute a method for processing tensor data for pattern recognition forsupervised learning under tensor mode; the method includes:

receiving an input training tensor data set;

introducing a within class scatter matrix into an objective functionsuch that between class distance is maximized, at the same time, withinclass distance is minimized by the objective function;

constructing an optimal frame of an objective function of an optimalprojection tensor machine subproblem;

transforming N vector modes of quadratic programming subproblems into amultiple quadratic programming problem under a single tensor mode, andconstructing an optimal frame of an objective function of an optimalprojection tensor machine problem;

obtaining a dual problem of the optimal frame of the objective function,introducing a tensor rank one decomposition into calculation of tensortransvection, and obtaining a revised dual problem according tolagrangian multiplier method;

utilizing sequential minimal optimization SMO algorithm to solve therevised dual problem and outputting an alagrangian optimal combinationand an offset scalar b;

calculating a projection tensor W_(*);

performing the rank one decomposition to the projection tensor W_(*);

performing a back projection to a component obtained after performingthe rank one decomposition to the projection tensor W_(*);

performing rank one decomposition inverse operation to the componentobtained after performing the back projection to obtain an optimalprojection tensor W which is corresponded to the training tensor dataset;

constructing a decision function construction phase and construct adecision function by the optimal projection tensor W which has beenrank-one decomposed together with the offset scalar b; and

inputting to-be-predicted tensor data which has been rank-one decomposedinto the decision function for prediction in an application predictionphase.

Furthermore, through an eta coefficient η, after the within classscatter introducing unit introduces the within class scatter matrix intoan objective function of an STM subproblem, the objection function ofthe quadratic programming problem of the n-th subproblem is changedinto:

${\min\limits_{w^{(n)},b^{(n)},\xi^{(n)}}{\frac{1}{2}\left\lbrack {\left( {{w^{(n)}}_{F}^{2} + {\eta\left( {\left( w^{(n)} \right)^{T}S_{w}^{(n)}w^{(n)}} \right)}} \right){\prod\limits_{1 < i < N}^{i \neq n}\;\left( {{w^{(i)}}_{F}^{2} + {\eta\left( {\left( w^{(i)} \right)^{T}S_{w}^{(n)}w^{(i)}} \right)}} \right)}} \right\rbrack}} + {C{\sum\limits_{m = 1}^{M}\;\xi_{m}^{(n)}}}$

wherein, S_(w) ^((n)) is an n-order within class scatter matrixestimated after the training tensor data set is expanded along the n-thorder; w^((n)) is the n-th order optimal projection vector of thetraining tensor data, n=1, 2, . . . N; C is a penalty factor; ξ_(m)^((n)) is a slack variable; eta coefficient η is configured to measurethe importance of the within class scatter matrix.

Furthermore, in the subproblem optimal frame constructing unit, theoptimal frame of the objective function of the OPSTM problem is acombination of N vector modes of quadratic programming problems, whichrespectively corresponds to a subproblem; wherein, a quadraticprogramming problem of the n-th subproblem is:

${\min\limits_{w_{*}^{(n)},b^{(n)},\xi^{(n)}}{\frac{1}{2}{w_{*}^{(n)}}_{F}^{2}{\prod\limits_{1 \leq i \leq N}^{i \neq n}\;{w_{*}^{(i)}}_{F}^{2}}}} + {C{\sum\limits_{m = 1}^{M}\;\xi_{m}^{(n)}}}$${y_{m}\left( {{\left( w_{*}^{(n)} \right)^{T}\left( {V_{m}{\prod\limits_{1 \leq i \leq N}^{i \neq n}\;{\times_{i}w_{*}^{(i)}}}} \right)} + b^{(n)}} \right)} \geq {1 - \xi_{m}^{(n)}}$S.t ξ_(m)^((n)) ≥ 0  m = 1, 2, …  M

wherein, w_(*) ^((n)) is the n-th order projection vector of thetraining tensor data set; w_(*) ^((n))=Λ^((n)1/2)P^((n)T)w^((n)),wherein Λ^((n)) and P^((n)) meet the equation, P^((n)T)(E+ηS_(w)^((n)))P^((n))=Λ^((n)); E is an identity matrix;

$V_{m} = {X_{m}{\prod\limits_{i = 1}^{N}{\times_{i}\left\lbrack \left( {P^{(i)}\Lambda^{{(i)}\;{1/2}}} \right)^{- 1} \right\rbrack^{T}}}}$is tensor input data obtained after tensor input data X_(m) in thetraining tensor data set is projected along each order; X_(i) is ani-mode multiplication operator; b^((n)) is the n-th order offset scalarof the training tensor data set.

Furthermore, according to a formula

${{W_{*}}_{F}^{2} = {\prod\limits_{n = 1}^{N}\;{w_{*}^{(n)}}_{F}^{2}}},$and a formula (w_(*) ^((n)))^(T)(V_(m)Π_(1<i<N) ^(i≠n)×_(i)w_(*)^((i)))=<W_(*), V_(m)>, the problem optimal frame constructing unittransforms the N vector modes of quadratic programming subproblems intothe multiple quadratic programming subproblem under a single tensormode. A constructed optimal frame of the objective function of the OPSTMproblem meets that:

${\min\limits_{{W_{*}b},\xi}{\frac{1}{2}{W_{*}}_{F}^{2}}} + {C{\sum\limits_{m = 1}^{M}\;\xi_{m}}}$y_(m)(⟨W_(*), V_(m)⟩ + b) ≥ 1 − ξ_(m) S.t ξ_(m) ≥ 0  m = 1, 2, …  M

wherein, < > is a transvection operator, and

$\xi_{m} = {\max\limits_{{n = 1},2,\;{\ldots\mspace{14mu} N}}{\left\{ \xi_{m}^{(n)} \right\}.}}$

Furthermore, according to lagrangian multiplier method, the dual problemsolving unit obtains the dual problem of the optimal frame of theobjective function, which is:

${\max\limits_{\alpha}{\sum\limits_{m = 1}^{M}\;\alpha_{m}}} - {\frac{1}{2}{\sum\limits_{i,{j = 1}}^{M}\mspace{11mu}{\alpha_{i}\alpha_{j}y_{i}y_{j}\left\langle {V_{i},V_{j}} \right\rangle}}}$${{\sum\limits_{m = 1}^{M}\;\left( {\alpha_{m}y_{m}} \right)} = {{{0{S.t}0} < a_{m} < {C\mspace{14mu} m}} = 1}},2,{{\ldots\mspace{14mu} M};}$

the dual problem solving unit introduces the tensor rank onedecomposition into the calculation of the tensor transvection. Anobtained revised dual problem is:

${{\max\limits_{\alpha}\mspace{14mu}{\sum\limits_{m = 1}^{M}\alpha_{m}}} - {\frac{1}{2}{\sum\limits_{i,{j = 1}}^{M}\;{\sum\limits_{p = 1}^{R}\;{\sum\limits_{q = 1}^{R}\;{\alpha_{i}\alpha_{j}y_{i}y_{j}{\prod\limits_{n = 1}^{N}\;{\left\langle {v_{ip}^{(n)},v_{jq}^{(n)}} \right\rangle{\sum\limits_{m = 1}^{M}\;\left( {\alpha_{m}y_{m}} \right)}}}}}}}}} = 0$S.t  0 < α_(m) < C  m = 1, 2, …  M.

Furthermore, the projection tensor calculating unit calculates theprojection tensor W_(*) according to a formula,

$W_{*} = {\sum\limits_{m = 1}^{M}\;{\alpha_{m}y_{m}{V_{m}.}}}$

In the embodiments of the present invention, N vector modes of quadraticprogramming problems are transformed into a multiple quadraticprogramming problem under a single tensor mode. The transformed optimalframe of the objective function is the optimal frame of the objectivefunction of the OPSTM problem. This can reduce the number of modelparameters significantly, overcome issues such as curse ofdimensionality, over learning and small amount of samples occurred whentraditional vector mode algorithms process the tensor data, whichensures efficient processing, at the same time, highlights excellentclassifying effects. Above all, the algorithms provided by theembodiments of the invention can process tensor data effectively anddirectly in tensor field, at the same time, possesses features ofoptimal classifying ability as well as strong practicability andpopularization.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an implementation flow chart of a method for processing tensordata for pattern recognition of the invention;

FIG. 2 is a system for processing tensor data for pattern recognition ofthe invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

In order to make the purposes, technical solutions and advantages of thepresent invention clearer, the invention is described hereinafter infurther details with reference to the drawings and embodiments. Itshould be understood that the specific embodiments described herein aremerely for explaining the invention, but not intended for limitation.

In one embodiment of the invention, receiving an input training tensordata set; introducing a within class scatter matrix into an objectivefunction such that between class distance is maximized, at the sametime, within class distance is minimized by the objective function;constructing an optimal frame of the objective function of an optimalprojection tensor machine OPSTM subproblem; constructing an optimalframe of an objective function of an OPSTM problem; according tolagrangian multiplier method, obtaining a dual problem of the optimalframe of the objective function, introducing a tensor rank onedecomposition into calculation of tensor transvection, and obtaining arevised dual problem; utilizing sequential minimal optimization SMOalgorithm to solve the revised dual problem and output a lagrangianoptimal combination and an offset scalar; calculating a projectiontensor; performing the rank one decomposition to the projection tensor;performing a back projection to a component obtained after performingthe rank one decomposition to the projection tensor; performing rank onedecomposition inverse operation to the component obtained afterperforming the back projection to obtain an optimal projection tensor Wwhich is corresponded to the training tensor data set; decision functionconstruction phase: by the optimal projection tensor W which has beenrank-one decomposed together with the offset scalar, constructing adecision function; application prediction phase: inputtingto-be-predicted tensor data which has been rank-one decomposed into thedecision function for prediction.

The implementation of the present invention will be described in detailwith reference to specific embodiments:

The First Embodiment

FIG. 1 shows an implementation process of a method for processing tensordata for pattern recognition, which is an optimization method forsupervised learning under tensor mode provided by the first embodimentof the present invention. The details are as follows:

Step 101, receiving an input training tensor data set.

In the embodiment of the invention, let the training tensor data set be{Xm, ym|m=1, 2 . . . M}, wherein X_(m) represents tensor input data,y_(m)∈{+1, −1} represents a label.

Take a gray level image for example, sample points are stored in a formof a second-order tensor (matrix), and all the sample points which arein a form of a column vector comprise an input data set. In a similarway, a label set is also a column vector; furthermore, the location ofeach label is corresponded to the location of the corresponding samplepoint.

$X = {{\begin{bmatrix}X_{1} \\X_{2} \\\vdots \\X_{M}\end{bmatrix}Y} = \begin{bmatrix}y_{1} \\y_{2} \\\vdots \\y_{M}\end{bmatrix}}$

Step 102, introducing a within class scatter matrix into an objectivefunction such that between class distance is maximized, at the sametime, within class distance is minimized by the objective function.

In the embodiment of the invention, the optimal frame of the objectivefunction of the support tensor machine (STM) problem is a combination ofN vector modes of quadratic programming problems, which respectivelycorrespond to a subproblem, wherein, a quadratic programming problem ofthe n-th subproblem is:

$\begin{matrix}{{\min\limits_{w^{(n)},b^{(n)},\xi^{(n)}}\mspace{14mu}{\frac{1}{2}{w^{(n)}}_{F}^{2}{\prod\limits_{1 \leq i \leq N}^{i \neq n}\;{w^{(i)}}_{F}^{2}}}} + {C{\sum\limits_{m = 1}^{M}\;\xi_{m}^{(n)}}}} & \left( {1\text{-}1} \right) \\{{{y_{m}\left( {{\left( w^{(n)} \right)^{T}\left( {X_{m}{\prod\limits_{1 \leq i \leq N}^{i \neq n}{\times_{i}w^{(i)}}}} \right)} + b^{(n)}} \right)} \geq {1 - \xi_{m}^{(n)}}}{S.t}} & \left( {1\text{-}2} \right) \\{{{\xi_{m}^{(n)} \geq {0\mspace{14mu} m}} = 1},2,{\ldots\mspace{14mu} M}} & \left( {1\text{-}3} \right)\end{matrix}$

wherein, w^((n)): the n-th order optimal projection vector of thetraining tensor data set, n=1, 2, . . . N;

b^((n)): the n-th order offset scalar of the training tensor data set,n=1, 2, . . . N;

C: a penalty factor;

ξ_(m) ^((n)): a slack variable.

After introducing the within class scatter matrix into an objectivefunction of an STM subproblem, through an eta coefficient η, theobjection function of the quadratic programming problem of the n-thsubproblem is changed into:

$\begin{matrix}{{\min\limits_{w^{(n)},b^{(n)},\xi^{(n)}}\mspace{14mu}{\frac{1}{2}\left\lbrack {\left( {{w^{(n)}}_{F}^{2} + {\eta\left( {\left( w^{(n)} \right)^{T}S_{w}^{(n)}w^{(n)}} \right)}} \right){\prod\limits_{1 < i < N}^{i \neq n}\;\left( {{w^{(i)}}_{F}^{2} + {\eta\left( {\left( w^{(i)} \right)^{T}S_{w}^{(n)}w^{(i)}} \right)}} \right)}} \right\rbrack}} + {C{\sum\limits_{m = 1}^{M}\;\xi_{m}^{(n)}}}} & \left( {1\text{-}4} \right)\end{matrix}$

wherein, S_(w) ^((n)) is the n-th order within class scatter matrixestimated after the training tensor data set is expanded along the n-thorder; w^((n)) herein possesses Fisher criterion effect, “maximumbetween class distance, minimum within class distance” at the n-th orderof the training tensor data set; eta coefficient η is configured tomeasure the importance of the within class scatter.

Step 103, constructing an optimal frame of the objective function of anoptimal projection tensor machine OPSTM subproblem.

In the embodiment of the invention, the optimal frame of an objectivefunction of an optimal projection tensor machine OPSTM problem is acombination of N vector modes of quadratic programming problems, whichrespectively correspond to a subproblem; wherein, a quadraticprogramming problem of the n-th subproblem is:

$\begin{matrix}{{\min\limits_{w_{*}^{(n)},b^{(n)},\xi^{(n)}}\mspace{14mu}{\frac{1}{2}{w_{*}^{(n)}}_{F}^{2}{\prod\limits_{1 \leq i \leq N}^{i \neq n}\;{w_{*}^{(i)}}_{F}^{2}}}} + {C{\sum\limits_{m = 1}^{M}\;\xi_{m}^{(n)}}}} & \left( {2\text{-}1} \right) \\{{{y_{m}\left( {{\left( w_{*}^{(n)} \right)^{T}\left( {V_{m}{\prod\limits_{1 \leq i \leq N}^{i \neq n}{\times_{i}w_{*}^{(i)}}}} \right)} + b^{(n)}} \right)} \geq {1 - \xi_{m}^{(n)}}}{S.t}} & \left( {2\text{-}2} \right) \\{{{\xi_{m}^{(n)} \geq {0\mspace{20mu} m}} = 1},2,{\ldots\mspace{14mu} M}} & \left( {2\text{-}3} \right)\end{matrix}$

wherein, w_(*) ^((n)): the n-th order projection vector of the trainingtensor data set; w_(*) ^((n))=Λ^((n)1/2)P^((n)T)w^((n)) n=1, 2, . . . N;w^((n)): the n-th order optimal projection vector of the training tensordata set of formula (1-4); Λ^((n)) and P^((n)) meet the equation,P^((n)T)(E+ηS_(w) ^((n)))P^((n))=Λ^((n)); E is an identity matrix;

$V_{m} = {X_{m}{\prod\limits_{i = 1}^{N}\;{\times_{i}\left\lbrack \left( {P^{(i)}\Lambda^{{(i)}{1/2}}} \right)^{- 1} \right\rbrack^{T}}}}$is tensor input data obtained after tensor input data X_(m) is projectedalong each order; X_(i) is an i-mode multiplication operator.

Step 104, transforming N vector modes of quadratic programmingsubproblems into a multiple quadratic programming problem under a singletensor mode, and constructing an optimal frame of an objective functionof an OPSTM problem.

In the embodiment of the invention,

$\begin{matrix}{{W_{*}}_{F}^{2} = {{{{w_{*}^{(1)} \circ w_{*}^{(2)} \circ \mspace{14mu}\ldots}\mspace{14mu} w_{*}^{(N)}}}_{F}^{2} = {{\sum\limits_{i_{1} = 1}^{I_{1}}\;{\sum\limits_{i_{2} = 1}^{I_{2}}\mspace{14mu}{\ldots\mspace{14mu}{\sum\limits_{i_{N} = 1}^{I_{N}}\; w_{*_{i_{1},{i_{2}\;\ldots\; i_{N}}}}^{2}}}}} = {{\sum\limits_{i_{1} = 1}^{I_{1}}\;{\sum\limits_{i_{2} = 1}^{I_{2}}\mspace{14mu}{\ldots\mspace{14mu}{\sum\limits_{i_{N} = 1}^{I_{N}}\;\left( {{w_{*_{i_{1}}}^{(1)} \cdot w_{*_{i_{2}}}^{(2)}}\mspace{14mu}\ldots\mspace{14mu} w_{*_{i_{N}}}^{(N)}} \right)^{2}}}}} = {{\left\langle {w_{*}^{(1)},w_{*}^{(1)}} \right\rangle\left\langle {w_{*}^{(2)},w_{*}^{(2)},} \right\rangle\mspace{14mu}\ldots\mspace{14mu}\left\langle {w_{*}^{(N)},w_{*}^{(N)}} \right\rangle} = {\prod\limits_{n = 1}^{N}\;{w_{*}^{(n)}}_{F}^{2}}}}}}} & {{Eq}.\mspace{14mu} 1} \\{{\left( w_{*}^{(n)} \right)^{T}\left( {V_{m}{\prod\limits_{i < i < N}^{i \neq n}\;{\times_{i}w_{*}^{(i)}}}} \right)} = {{V_{m} \times_{1}w_{*}^{(1)} \times_{2}w_{*}^{(2)} \times \ldots \times_{({n - 1})}w_{*}^{({n - 1})} \times_{n}w_{*}^{(n)} \times {{}_{\left( {n + 1} \right)}^{}{}_{}^{\left( {n + 1} \right)}}\mspace{14mu}\ldots \times_{N}w_{*}^{(N)}} = {{\sum\limits_{i_{1} = 1}^{I_{1}}\;{\sum\limits_{i_{2} = 1}^{I_{2}}\mspace{14mu}{\ldots\mspace{14mu}{\sum\limits_{i_{N} = 1}^{I_{N}}\;{v_{m,i_{1},i_{2},\;{\ldots\mspace{14mu} i_{N}}}w_{*_{i_{1}}}^{(1)}w_{*_{i_{2}}}^{(2)}\mspace{14mu}\ldots\mspace{14mu} w_{*_{i_{N}}}^{(N)}}}}}} = {{\sum\limits_{i_{1} = 1}^{I_{1}}\;{\sum\limits_{i_{2} = 1}^{I_{2}}\mspace{14mu}{\ldots\mspace{14mu}{\sum\limits_{i_{N} = 1}^{I_{N}}\;{v_{m,i_{1},i_{2},\;{\ldots\mspace{14mu} i_{N}}}w_{*_{i_{1},i_{2},\;{\ldots\mspace{14mu} i_{N}}}}}}}}} = {\left\langle {W_{*},V_{m}} \right\rangle.}}}}} & {{Eq}.\mspace{14mu} 2}\end{matrix}$

wherein, ∥ ∥_(F) ² represents a norm and “∘” represents an outer productoperator. According to the formulas, Eq. 1 and Eq. 2,

${{W_{*}}_{F}^{2} = {\prod\limits_{n = 1}^{N}\;{w_{*}^{(n)}}_{F}^{2}}},$and (w_(*) ^((n)))^(T)(V_(m)Π_(1<i<N) ^(i≠n)×_(i)w_(*) ^((i)))=<W_(*),V_(m)>. Therefore, vector mode of quadratic programming problems of Nsubproblems can be transformed into a multiple quadratic programmingproblem under a single tensor mode, which means the optimal frame of anobjective function of an OPSTM problem is:

$\begin{matrix}{{\min\limits_{W_{*},b,\xi}\mspace{14mu}{\frac{1}{2}{W_{*}}_{F}^{2}}} + {C{\sum\limits_{m = 1}^{M}\;\xi_{m}}}} & \left( {3\text{-}1} \right) \\{{{S.t}\mspace{14mu}{y_{m}\left( {\left\langle {W_{*},V_{m}} \right\rangle + b} \right)}} \geq {1 - \xi_{m}}} & \left( {3\text{-}2} \right) \\{{{\xi_{m} \geq {0\mspace{14mu} m}} = 1},2,{\ldots\mspace{14mu} M}} & \left( {3\text{-}3} \right)\end{matrix}$

wherein, W_(*) is a projection tensor; < > is a transvection operator,and

$\xi_{m} = {\max\limits_{{n = 1},2,\;{\ldots\mspace{14mu} N}}{\left\{ \xi_{m}^{(n)} \right\}.}}$

Through the Eq. 1 and Eq. 2, N vector modes of quadratic programmingproblems are transformed into a multiple quadratic programming problemunder a single tensor mode. The transformed optimal frame of theobjective function is the optimal frame of the objective function of theOPSTM problem. This can reduce the number of model parameterssignificantly, overcome issues such as curse of dimensionality, overlearning and small sample occurred when vector mode algorithms processthe tensor data.

Step 105, according to lagrangian multiplier method, obtaining a dualproblem of the optimal frame of the objective function, introducing atensor rank one decomposition into calculation of tensor transvection,and obtaining a revised dual problem.

In the embodiment, according to lagrangian multiplier method, a dualproblem of the optimal frame [(3-1), (3-2), (3-3)] of the objectionfunction of the OPSTM problem is obtained, wherein α_(m) is a lagrangianmultiplier.

$\begin{matrix}{{\max\limits_{\alpha}\mspace{14mu}{\sum\limits_{m = 1}^{M}\;\alpha_{m}}} - {\frac{1}{2}{\sum\limits_{i,{j = 1}}^{M}\;{\alpha_{i}\alpha_{j}y_{i}y_{j}\left\langle {V_{i},V_{j}} \right\rangle}}}} & \left( {4\text{-}1} \right) \\{{{\sum\limits_{m = 1}^{M}\;\left( {\alpha_{m}y_{m}} \right)} = 0}{S.t}} & \left( {4\text{-}2} \right) \\{{{0 < \alpha_{m} < {C\mspace{14mu} m}} = 1},2,{\ldots\mspace{14mu} M}} & \left( {4\text{-}3} \right)\end{matrix}$

A tensor CP (CANDECOMP/PARAFAC) is decomposed and introduced to thecalculation of tensor transvection.

Rank one decompositions of tensor data V_(i), V_(j) are respectively:

$V_{i} = {\sum\limits_{r = 1}^{R}\;{v_{ir}^{(1)} \circ v_{ir}^{(2)} \circ \ldots \circ v_{ir}^{(N)}}}$$V_{j} = {\sum\limits_{r = 1}^{R}\;{{v_{jr}^{(1)} \circ v_{jr}^{(2)} \circ \ldots \circ v_{jr}^{(N)}}\mspace{14mu}{and}}}$$\left\langle {V_{i},V_{j}} \right\rangle = {\sum\limits_{p = 1}^{R}\;{\sum\limits_{q = 1}^{R}\;{\prod\limits_{n = 1}^{N}\;\left\langle {v_{ip}^{(n)},v_{jq}^{(n)}} \right\rangle}}}$

Therefore, the dual problem can be changed into:

$\begin{matrix}{{\max\limits_{\alpha}\mspace{14mu}{\sum\limits_{m = 1}^{M}\;\alpha_{m}}} - {\frac{1}{2}{\sum\limits_{i,{j = 1}}^{M}\;{\sum\limits_{p = 1}^{R}\;{\sum\limits_{q = 1}^{R}\;{\alpha_{i}\alpha_{j}y_{i}y_{j}{\prod\limits_{n = 1}^{N}\;\left\langle {v_{ip}^{(n)},v_{jq}^{(n)}} \right\rangle}}}}}}} & \left( {4\text{-}4} \right) \\{{{\sum\limits_{m = 1}^{M}\;\left( {\alpha_{m}y_{m}} \right)} = 0}{S.t}} & \left( {4\text{-}2} \right) \\{{{0 < \alpha_{m} < {C\mspace{14mu} m}} = 1},2,{\ldots\mspace{14mu} M}} & \left( {4\text{-}3} \right)\end{matrix}$

In the objection function (4-1) of the dual problem, a tensor rank onedecomposition auxiliary calculation,

${\left\langle {V_{i},V_{j}} \right\rangle = {\sum\limits_{p = 1}^{R}\;{\sum\limits_{q = 1}^{R}\;{\prod\limits_{n = 1}^{N}\;\left\langle {v_{ip}^{(n)},v_{jq}^{(n)}} \right\rangle}}}},$is introduced into the tensor transvection calculation part, whichfurther reduces calculation complexity and storage cost, at the sametime, the tensor rank one decomposition can obtain a more compact andmore meaningful representation of a tensor objection, extract structuralinformation and internal correlation of the tensor data moreeffectively, and avoid a time-consuming alternative projection iterativeprocess of the tensor mode algorithms of the prior art.

Step 106, utilizing sequential minimal optimization SMO algorithm tosolve the revised dual problem and output an alagrangian optimalcombination α=[α₁, α₂, . . . α_(M)] and an offset scalar b.

Step 107, calculating a projection tensor W_(*).

In the embodiment of the invention, the projection tensor W_(*) iscalculated according to the formula

$W_{*} = {\sum\limits_{m = 1}^{M}{\alpha_{m}y_{m}{V_{m}.}}}$

Step 108, performing the rank one decomposition to the projection tensorW_(*).

In the embodiment of the invention, the rank one decomposition isperformed to the projection tensor W_(*), and the formula W_(*)=w_(*)⁽¹⁾∘w_(*) ⁽²⁾∘ . . . w_(*) ^((N)) is obtained.

Step 109, performing a back projection to a component obtained afterperforming the rank one decomposition to the projection tensor W_(*).

In the embodiment of the invention, the back projection to a componentis performed after performing the rank one decomposition to theprojection tensor W_(*) to obtain the formulaw^((n))=(Λ^((n)1/2)P^((n)))⁻¹w_(*) ^((n)), wherein w^((n)) correspondsto the optimal projection vector of (1-4), and is the n-th order optimalprojection vector of the training tensor data set, n=1, 2, . . . N.

Step 110, performing rank one decomposition inverse operation to thecomponent obtained after performing the back projection to obtain anoptimal projection tensor W which is corresponded to the training tensordata set.

In the embodiment of the invention, the components obtained afterperforming back projection are blended (rank one decomposition inverseoperation) into the optimal projection tensor W, W=w⁽¹⁾∘w⁽²⁾∘ . . .w^((N)). therefore, the optimal projection tensor W can embody Fishercriterion at each order.

Step 111, decision function construction phase: by the optimalprojection tensor W which has been rank-one decomposed together with theoffset scalar b, constructing a decision function.

In the embodiment of the invention, at the decision functionconstruction phase, the rank one decomposition should be performed tothe optimal projection tensor W, the decomposed optimal projectiontensor W and the offset scalar b are used for constructing the decisionfunction:

${y(X)} = {{{sign}\left\lbrack {{{\prod\limits_{n = 1}^{N}{\sum\limits_{p = 1}^{R}\sum\limits_{q = 1}^{R}}} < w_{p}^{(n)}},{x_{q}^{(n)} > {+ b}}} \right\rbrack}.}$

Step 112, at the application prediction phase, inputting to-be-predictedtensor data which has been rank-one decomposed into the decisionfunction for prediction.

In the embodiment of the invention, at the application prediction phase,the to-be-predicted tensor data which has been performed rank-onedecomposed is input into the decision function for prediction.

Compared with the prior art, the embodiment possesses the followingadvantages: 1) N vector modes of quadratic programming problems aretransformed into a multiple quadratic programming problem under a singletensor mode. The optimal frame of the transformed objective function isthe optimal frame of the objective function of the OPSTM problem. Thiscan reduce the number of model parameters significantly, overcome issuessuch as curse of dimensionality, over learning and small sample occurredwhen traditional vector mode algorithms process the tensor data, whichensures high-activity processing, at the same time, highlights excellentclassifying effects. Above all, the algorithms provided by theembodiments of the invention can process tensor data effectively anddirectly in tensor field, at the same time, possesses a feature ofoptimal classifying ability as well as strong practicability andpopularization. 2) the within scatter matrix is introduced into theobject function, which can receive and process the tensor data directlyin the tensor field, and the output optimal projection tensor W canembody the Fisher criterion effect, “maximum between class distance,minimum within class distance” at each order. 3) In the objectionfunction (4-1) of the dual problem, a tensor rank one decompositionauxiliary calculation,

${\left\langle {V_{i},V_{j}} \right\rangle = {\sum\limits_{p = 1}^{R}{\sum\limits_{q = 1}^{R}{\prod\limits_{n = 1}^{N}\left\langle {v_{ip}^{(n)},v_{jq}^{(n)}} \right\rangle}}}},$is introduced into the tensor transvection calculation part, whichfurther reduces calculation complexity and storage cost, at the sametime, the tensor rank one decomposition can obtain a more compact andmore meaningful representation of the tensor objection, and extractstructural information and internal correlation of the tensor data moreeffectively, and avoid a time-consuming alternative projection iterativeprocess.

It should be understood that the serial number of each step in thisembodiment does not signify the execution sequence; the executionsequence of each step should be determined according to its function andinternal logic, and should not form any limitation to the implementationprocess of the embodiment of the invention.

It should be understood by those skilled in the art that the whole orpartial steps of the methods in each embodiment can be achieved byrelevant hardware instructed by program, and the corresponding programcan be stored in a computer-readable storage medium; the storage mediumcan be for example ROM/RAM, magnetic disk or light disk, etc.

The Second Embodiment

FIG. 2 shows a specific structural block diagram of a system forprocessing tensor data for pattern recognition provided by the secondembodiment of the invention. For illustration purposes, merely the partrelevant to the embodiment of the invention is shown. The optimizationsystem 2 for supervised learning under tensor mode includes: a datareceiving unit 21, a within class scatter introducing unit 22, asubproblem optimal frame constructing unit 23, a problem optimal frameconstructing unit 24, a dual problem obtaining unit 25, a dual problemsolving unit 26, a projection tensor calculating unit 27, a projectiontensor decomposition unit 28, a back projection unit 29, an optimalprojection tensor calculating unit 210, a decision function constructingunit 211 and a predicting unit 212.

The data receiving unit 21 is configured to receive an input trainingtensor data set;

The within class scatter introducing unit 22 is configured to introducea within class scatter matrix into an objective function such thatbetween class distance is maximized, at the same time, within classdistance is minimized by the objective function;

The subproblem optimal frame constructing unit 23 is configured toconstruct an optimal frame of an objective function of an optimalprojection tensor machine OPSTM subproblem;

The problem optimal frame constructing unit 24 is configured totransform N vector modes of quadratic programming subproblems into amultiple quadratic programming problem under a single tensor mode, andconstruct an optimal frame of an objective function of an OPSTM problem;

The dual problem obtaining unit 25 is configured to obtain a dualproblem of the optimal frame of the objective function, introduce tensorrank one decomposition into calculation of tensor transvection, andobtain a revised dual problem according to lagrangian multiplier method;

The dual problem solving unit 26 is configured to utilize sequentialminimal optimization SMO algorithm to solve the revised dual problem andoutput a lagrangian optimal combination and an offset scalar b;

The projection tensor calculating unit 27 is configured to calculate aprojection tensor W_(*);

The projection tensor decomposition unit 28 is configured to perform therank one decomposition to the projection tensor W_(*);

The back projection unit 29 is configured to perform a back projectionto a component obtained after performing the rank one decomposition tothe projection tensor W_(*);

The optimal projection tensor calculating unit 210 is configured toperform rank one decomposition inverse operation to the componentobtained after performing the back projection to obtain an optimalprojection tensor W which is corresponded to the training tensor dataset;

The decision function constructing unit 211 is configured to construct adecision function construction phase and construct a decision functionby the optimal projection tensor W which has been rank-one decomposedtogether with the offset scalar b;

The predicting unit 212 is configured to input to-be-predicted tensordata which has been rank-one decomposed into the decision function forprediction in the application prediction phase.

Furthermore, through an eta coefficient η, after the within classscatter introducing unit 22 introduces the within class scatter matrixinto an objective function of an STM subproblem, the objection functionof the quadratic programming problem of the n-th subproblem is changedinto:

${\min\limits_{w^{(n)},b^{(n)},\xi^{(n)}}{\frac{1}{2}\left\lbrack {\left( {{w^{(n)}}_{F}^{2} + {\eta\left( {\left( w^{(n)} \right)^{T}S_{w}^{(n)}w^{(n)}} \right)}} \right){\prod\limits_{1 < i < N}^{i \neq n}\left( {{w^{(i)}}_{F}^{2} + {\eta\left( {\left( w^{(i)} \right)^{T}S_{w}^{(n)}w^{(i)}} \right)}} \right)}} \right\rbrack}} + {C{\sum\limits_{m = 1}^{M}\xi_{m}^{(n)}}}$

wherein, S_(w) ^((n)) is an n-order within class scatter matrixestimated after the training tensor data set is expanded along the n-thorder; w^((n)) is the n-th order optimal projection vector of thetraining tensor data, n=1, 2, . . . N; C is a penalty factor; ξ_(m)^((n)) is a slack variable; eta coefficient η is configured to measurethe importance of the within class scatter matrix.

Furthermore, in the subproblem optimal frame constructing unit 23, theoptimal frame of the objective function of the OPSTM problem is acombination of N vector modes of quadratic programming problems, whichrespectively corresponds to a subproblem; wherein a quadraticprogramming problem of the n-th subproblem is:

${\min\limits_{w_{*}^{(n)},b^{(n)},\xi^{(n)}}{\frac{1}{2}{w_{*}^{(n)}}_{F}^{2}{\prod\limits_{1 \leq i \leq N}^{i \neq n}{w_{*}^{(i)}}_{F}^{2}}}} + {C{\sum\limits_{m = 1}^{M}\xi_{m}^{(n)}}}$${{{S.t.\mspace{14mu}{y_{m}\left( {{\left( w_{*}^{(n)} \right)^{T}\left( {V_{m}{\prod\limits_{1 \leq i \leq N}^{i \neq n}{\times_{i}w_{*}^{(i)}}}} \right)} + b^{(n)}} \right)}} \geq {1 - {\xi_{m}^{(n)}\xi_{m}^{(n)}}} \geq {0\mspace{14mu} m}} = 1},2,{\ldots\mspace{14mu} M}$wherein, w_(*) ^((n)) is the n-th order projection vector of thetraining tensor data set; w_(*) ^((n))=Λ^((n)1/2)P^((n)T)w^((n)),wherein Λ^((n)) and P^((n)) meet the equation, P^((n)T)(E+ηS_(w)^((n)))P^((n))=Λ^((n)); E is an identity matrix;

$V_{m} = {X_{m}{\prod\limits_{i = 1}^{N}{\times_{i}\left\lbrack \left( {P^{(i)}\Lambda^{{(i)}{1/2}}} \right)^{- 1} \right\rbrack^{T}}}}$is tensor input data obtained after tensor input data X_(m) in thetraining tensor data set is projected along each order; X_(i) is ani-mode multiplication operator; b^((n)) is the n-th order offset scalarof the training tensor data set.

Furthermore, according to a formula

${{W_{*}}_{F}^{2} = {\prod\limits_{n = 1}^{N}{w_{*}^{(n)}}_{F}^{2}}},$and a formula (w_(*) ^((n)))^(T)(V_(m)Π_(1<i<N) ^(i≠n)×_(i)w_(*)^((i)))=<W_(*), V_(m)>, the problem optimal frame constructing unit 24transforms the N vector modes of quadratic programming subproblems intothe multiple quadratic programming subproblem under a single tensormode. A constructed optimal frame of the objective function of the OPSTMproblem meets that:

${\min\limits_{W_{*},b,\xi}{\frac{1}{2}{W_{*}}_{F}^{2}}} + {C{\sum\limits_{m = 1}^{M}\xi_{m}}}$S.t.  y_(m)(⟨W_(*), V_(m)⟩ + b) ≥ 1 − ξ_(m)ξ_(m) ≥ 0  m = 1, 2, …  M

wherein, < > is a transvection operator, and

$\xi_{m} = {\max\limits_{{n = 1},2,{\ldots\mspace{14mu} N}}{\left\{ \xi_{m}^{(n)} \right\}.}}$

Furthermore, according to lagrangian multiplier method, the dual problemsolving unit 26 obtains the dual problem of the optimal frame of theobjective function, which is:

${\max\limits_{\alpha}{\sum\limits_{m = 1}^{M}\alpha_{m}}} - {\frac{1}{2}{\sum\limits_{i,{j = 1}}^{M}{\alpha_{i}\alpha_{j}y_{i}y_{j}\left\langle {V_{i},V_{j}} \right\rangle}}}$${S.t.\mspace{14mu}{\sum\limits_{m = 1}^{M}\left( {\alpha_{m}y_{m}} \right)}} = 0$0 < α_(m) < C  m = 1, 2, …  M.

The dual problem solving unit 26 introduces the tensor rank onedecomposition into the calculation of the tensor transvection. Anobtained revised dual problem is:

${\max\limits_{\alpha}{\sum\limits_{m = 1}^{M}\alpha_{m}}} - {\frac{1}{2}{\sum\limits_{i,{j = 1}}^{M}{\sum\limits_{p = 1}^{R}{\sum\limits_{q = 1}^{R}{\alpha_{i}\alpha_{j}y_{i}y_{j}{\prod\limits_{n = 1}^{N}\left\langle {V_{ip}^{(n)},V_{jq}^{(n)}} \right\rangle}}}}}}$${S.t.\mspace{14mu}{\sum\limits_{m = 1}^{M}\left( {\alpha_{m}y_{m}} \right)}} = 0$0 < α_(m) < C  m = 1, 2, …  M.

Furthermore, the projection tensor calculating unit 27 calculates theprojection tensor W_(*) according to a formula,

$W_{*} = {\sum\limits_{m = 1}^{M}{\alpha_{m}y_{m}{V_{m}.}}}$

The optimization system for supervised learning under tensor modeprovided by the embodiment of the invention can be applied to thecorresponding method of the first embodiment. Please refer to thedescription of the first embodiment, which would not be furtherdescribed herein.

Those skilled in the art should understand that the exemplary units andalgorithm steps described in accompany with the embodiments disclosed inthe specification can be achieved by electronic hardware, or thecombination of computer software with electronic hardware. Whether thesefunctions are executed in a hardware manner or a software manner dependson the specific applications and design constraint conditions of thetechnical solutions. With respect to each specific application, aprofessional technician can achieve the described functions utilizingdifferent methods, and these achievements should not be deemed as goingbeyond the scope of the invention.

Those skilled in the art can be clearly understood that for convenienceand briefness, the specific working process of the described system,apparatus and unit can refer to the corresponding process of the abovemethod embodiment, which would be further described herein.

It should be understood that the systems, devices and methods disclosedin several embodiments provided by the present application can beachieved in alternative ways. For example, the described deviceembodiments are merely schematically. For example, the division of theunits is merely a division based on logic function, whereas the unitscan be divided in other ways in actual realization; for example, aplurality of units or components can be grouped or integrated intoanother system, or some features can be omitted or not executed.Furthermore, the shown or discussed mutual coupling or direct couplingor communication connection can be achieved by indirect coupling orcommunication connection of some interfaces, devices or units inelectric, mechanical or other ways.

The units described as isolated elements can be or not be separatedphysically; an element shown as a unit can be or not be physical unit,which means that the element can be located in one location ordistributed at multiple network units. Some or all of the units can beselected according to actual needs to achieve the purpose of the schemesof the embodiments.

Furthermore, each functional unit in each embodiment of the presentinvention can be integrated into a processing unit, or each unit canexist in isolation, or two or more than two units can be integrated intoone unit.

If the integrated unit is achieved in software functional unit and soldor used as an independent product, the integrated unit can be stored ina computer-readable storage medium. Based on this consideration, thesubstantial part, or the part that is contributed to the prior art ofthe technical solution of the present invention, or part or all of thetechnical solutions can be embodied in a software product. The computersoftware product is stored in a storage medium, and includes severalinstructions configured to enable a computer device (can be a personalcomputer, device, network device, and so on) to execute all or some ofthe steps of the method of each embodiment of the present invention. Thestorage medium includes a U disk, a mobile hard disk, a read-only memory(ROM, Read-Only Memory), a random access memory (RAM, Random AccessMemory), a disk or a light disk, and other various mediums which canstore program codes.

The above contents are merely specific embodiments of the presentinvention, however, the protection scope of the present invention shouldnot be limited by this. Any person skilled in the art can easilyenvisage alternations and displacements within the technical scopedisclosed by the invention, which should also be within the protectionscope of the present invention. Therefore, the protection scope of thepresent invention should be subjected to the protection scope of theclaims.

What is claimed is:
 1. A method for processing tensor data for patternrecognition, wherein the method comprises: receiving an input trainingtensor data set; introducing a within class scatter matrix into anobjective function such that between class distance is maximized, at thesame time, within class distance is minimized by the objective function;constructing an optimal frame of the objective function of an optimalprojection tensor machine subproblem; transforming N vector modes ofquadratic programming subproblems into a multiple quadratic programmingproblem under a single tensor mode, and constructing an optimal frame ofan objective function of an optimal projection tensor machine problem;according to lagrangian multiplier method, obtaining a dual problem ofthe optimal frame of the objective function, introducing a tensor rankone decomposition into calculation of tensor transvection, and obtaininga revised dual problem; utilizing sequential minimal optimizationalgorithm to solve the revised dual problem and output an alagrangianoptimal combination and an offset scalar b; calculating a projectiontensor W_(*); performing the rank one decomposition to the projectiontensor W_(*); performing a back projection to a component obtained afterperforming the rank one decomposition to the projection tensor W_(*);performing rank one decomposition inverse operation to the componentobtained after performing the back projection to obtain an optimalprojection tensor W which is corresponded to the training tensor dataset; decision function construction phase: by the optimal projectiontensor W which has been rank-one decomposed together with the offsetscalar b, constructing a decision function; application predictionphase: inputting to-be-predicted tensor data which has been rank-onedecomposed into the decision function for prediction.
 2. A computerdevice, comprising a storage medium with computer instructions storedthereon, wherein the computer instructions are configured to enable thecomputer device to execute a method for processing tensor data forpattern recognition, wherein the method comprises: receiving an inputtraining tensor data set; introducing a within class scatter matrix intoan objective function such that between class distance is maximized, atthe same time, within class distance is minimized by the objectivefunction; constructing an optimal frame of an objective function of anoptimal projection tensor machine subproblem; transforming N vectormodes of quadratic programming subproblems into a multiple quadraticprogramming problem under a single tensor mode, and constructing anoptimal frame of an objective function of an optimal projection tensormachine problem; obtaining a dual problem of the optimal frame of theobjective function, introducing a tensor rank one decomposition intocalculation of tensor transvection, and obtaining a revised dual problemaccording to lagrangian multiplier method; utilizing sequential minimaloptimization algorithm to solve the revised dual problem and outputtingan alagrangian optimal combination and an offset scalar b; calculating aprojection tensor W_(*); performing the rank one decomposition to theprojection tensor W_(*); performing a back projection to a componentobtained after performing the rank one decomposition to the projectiontensor W_(*); performing rank one decomposition inverse operation to thecomponent obtained after performing the back projection to obtain anoptimal projection tensor W which is corresponded to the training tensordata set; constructing a decision function by the optimal projectiontensor W which has been rank-one decomposed together with the offsetscalar b; and inputting to-be-predicted tensor data which has beenrank-one decomposed into the decision function for prediction in anapplication prediction phase.